Measuring the flow rate is an important aspect in all industries. There are several ways tomeasure the flow of fluids in pipes.Objectives:1. Measure the flow of water using different flow meters (Orifice plate flow meter andmeasuring nozzle, Pitot tube, Venturi nozzle and rotameter) by applying Bernoullisprinciple2. Investigate the relationship between flow and pressure through different flow meters3. Determine the corresponding discharge coefficients (Cd) for each flow meters1.1

Theory on Venturi meter

The Venturi meter is a device for measuring discharge in a pipe. It consists of a rapidlyconverging section (denoted as point 2 in Figure 1) which increases the velocity of flowand hence reduces the pressure. It then returns to the original dimensions of the pipe by agently diverging the diffuser. By measuring the pressure differences, the dischargecoefficient can be calculated. This is a particularly accurate method of flow measurementas energy loss is very small.

Figure 1: Schematic representation of a Venturi meter

Referring to the above Venturi tube diagram, the Bernoulli equation can be applied topoints 1 and 2. Following the analysis, the equations for flow rate can be derived.Volumetric flow rate:

Qth= A V3 3

2g

A 3

h1

1-

A1

where:

Qth

theoretical volumetric flow rate (m /s)

2cross sectional area at 1 (m )cross sectional area at 3 (m2)height of manometer column 1 in meters (m)height of manometer column 3 in meters (m)

A1A3h1h3

The discharge coefficient is defined as the ratio of actual volume flow rate to theoreticalvolume flow rate:Coefficient of discharge, Cd = Qactual/QtheoreticalThe discharge coefficient is less than unity due to the losses caused by the wall shear stress,the losses in contraction and the losses during expansion.Q

act

C Qd

th

h3

A 2

31 A

2g= Cd A3

h1

dA 3

and Qact n h ..........where n C

2g A 3 2

1 A 1

h1 h3

2g3 A 3 2

1 A 1

This equation can be written as:

Orifice Plate Meter

An orifice plate is a restriction with an opening smaller than the pipe diameter which isinserted in the pipe; the typical orifice plate has a concentric, sharp edged opening, asshown in Figure 2. Because of the smaller area the fluid velocity increases, causing acorresponding decrease in pressure. The flow rate can be calculated from the measuredpressure drop across the orifice plate, P1-P3. The orifice plate is the most commonly usedflow sensor, but it creates a rather large non-recoverable pressure due to the turbulencearound the plate, leading to high energy consumption.

Figure 2: Schematic representation of Orifice meter

Referring to the orifice plate diagram, the Bernoulli equation can be applied to points 1and 3. Following the analysis, the equations for volumetric flow rate can be expressed asthe following:

Qth

where:

Qtham

=a

2g h

2 1-m

theoretical volumetric flow rate (m /s)

2cross-sectional area of plate (m )ratio of cross-sectional area of plate to pipe, (a/A)difference in height of manometer column (m)

The discharge coefficient is defined as the ratio of actual volume flow rate to theoreticalvolume flow rate:Coefficient of discharge, Cd = Qactual/Qtheoretical

act

C Q

d th 2g h

=C a

and Q

1.3

1-m

act C

aA

2- a 2 d A

2g

C a

1-

a A

2g h

..........where

aA

A 2-a 2

meter coefficient

Pitot and Pitot Static Tube

A Pitot tube is a simple device used to measure flow rates. It works for both liquid andgas flows. The device, in its simplest form, consists of a small diameter hollow tube bentinto the shape of a L. Usually the upstream opening is smaller than the diameter of thetube. The height, above the center-line, of the fluid in the in the vertical leg of the tube isrelated to the velocity of the fluid in the flow. Pitot tubes (also called Pitot probes) andPitot-static tubes are widely used for flow speed measurement. A Pitot tube is just a tubewith a pressure tap at the stagnation point that measures stagnation pressure, while aPitot-static probe has both a stagnation pressure tap and several circumferential staticpressure taps and it measures both stagnation and static pressures. Figure 3 illustrates thetypes of Pitot tubes.

Figure 3: a) A Pitot probe measures stagnation pressure at the nose of the probe, while(b) a Pitot-static probe measures both stagnation pressure and static pressure, from whichthe flow speed is calculated.

Figure 4: Illustration of stagnation point at the opening of a Pitot probe

Referring to Figure 4, writing the Bernoullis equation between points 1 and 2:

P v2 z P v2 g 2g g 2g z1

and zeroing out z1, z2, and v2 we get

P v2 P2

2g

Assigning values to the various parameters

Pgd

and P g(d h)

Substituting into the Bernoulli equation, neglecting friction, andsolving for v1 we obtain,v22g

PPo

g(d h) g d

Therefore, (theoretical velocity) is

v 2 g h6

Where h is head difference measured.

The difference between the Pitot tube and the static Pitot tube is the small opening on theside of the submerged part of the tube. Unlike the stagnation tube, a direct measurementof P is possible. Using the Bernoulli equation and neglecting friction:P 1

v2

z P 1

g 2ggP P v2

2g

g g

v2 z

2g

Pv 2

The value of v calculated through the above equation is called theoretical value.However, the actual value is calculated as:v c 2gh or v c

EXPERIMENTAL & METHODS

2.1

Apparatus

The flow measurement experiment apparatus (Figure 5) comprises a Venturi nozzle (9),an orifice plate, a measuring nozzle and a Pitot tube (8) for flow measurement and arotameter (3). The flow rate can be regulated using the gate valve (2). The pressure lossesat the measuring elements can be recorded using pressure connections with rapid actioncouplings. The connections are connected to a six-tube manometer (6), which is fittedwith a ventilation valve. The six-tube manometer is used in order to determine thepressure distribution in the Venturi nozzle or the orifice plate flow meter and measuringnozzle. The total pressure is measured by a Pitot tube.

1mbar). The measuring range is 390 mmWC. All the tubes are connected to one another

at the upper end and ventilated by a shared ventilation valve (12). The measuringconnections (10) are at the lower end. Differential pressure measurements are carried outwith the ventilation valve closed (12, 13), while relative gauge pressure measurementswith the ventilation valve open (12). Standard pressure unit is Pascal (Pa), where 1Pa =2

1N/m = 10-5bar = 0.01mbar

Figure 6: Illustration of multi-tube manometer

Equating the pressure at the level (pressure at the same level in a continuous body ofstatic fluid is equal),For the left hand side:p1 p A gh1For the right hand side:p2 p A gh2Pressure difference, pp p1 p2 p A gh1 p A gh2p p1 p2 g(h1 h2 )Rotameter in this apparatus consists of a vertical conical measuring section, throughwhich the liquid flows from bottom to top. A specially shaped float moves freely in theliquid flow and is carried along by the flow due to its flow resistance. This results inequilibrium between the weight of the float on the one hand and its drag and lifting forceon the other. The float adjusts to a particular height in the measuring tube depending on9

the flow volume. Because of the operating principle, a reliable measuring range on arotameter never begins at zero, but at 5-10% of the final measuring value. The measuredflow rate value is always read at the upper edge of the float. The maximum flowmeasured by the rotameter is 1,600 L/h.

Figure 7: Technique to read the measurement of a rotameter.

2.2

Experimental Procedure1. Make sure all six manometer tubes are attached to the Venturi meter andmanometer panel.2. Switch on the pump. Turn the gate valve open (slowly) then open themanometers ventilation valve (12) (Let the water runs for a moment to release airbubbles from the system).3. Once bubbles are no more visible (from the manometer columns and connectingtubes), close the gate valve followed by manometers ventilation valve (12) andthen switch of the pump.4. Open the manometers air ventilation valve (13) slowly while monitoring thewater level in the manometer tubes drop. Close the valve when the water level inthe manometer column reaches 30-40 mmWC.5. To begin the experiment, switch on the pump and open the gate valve slowly. Theflow of water is controlled by the gate valve.6. Set the rotameter at a certain value. Monitor the changes in water column. Makesure the water levels in all six tubes are within the measuring range (0-390mmWC).7. Repeat the measurement of manometer levels with different flows by controllingthe gate valve opening (minimum flow 200 L/h)8. When the measurement is done, switch off the pump.9. The experiment is continued with flow measurement by Orifice plate, nozzle andPitot tube. Similar procedure is applied.10

3.0

RESULTS & DISCUSSION

For all flow measuring meter:

1.

Discuss the trend of manometer water level respective to different flow meter.

2. Demonstrate the relationship between flow and pressure using Bernoulli principle(plot graph).3.